Assume that a 25-year-old man has these probabilities of dying during the next f

Question

Assume that a 25-year-old man has these probabilities of dying during the next five years. What is the probability that the man does not die in the next five years? (Enter your answer to five decimal places.) _____ An online insurance site offers a term insurance policy that will pay $100,000 if a 25-year-old man dies within the next 5 years. The cost is $170 per year. So the insurance company will take in $850 from this policy if the man does not die within five years. If he does die, the company must pay $100,000. Its loss depends on how many premiums were paid, as follows. What is the insurance company's mean cash intake from such polices? () $ _____

Explanation / Answer

(a)We are provided with the probabilities of dying at different ages for next 5 years

Probability that the person does not die in next five years = (1-P(x=25))*(1-P(x=26))*(1-P(x=27))*(1-P(x=28))*(1-P(x=29))

=(1-0.00036)*(1-0.00043)**(1-0.00053)*(1-0.00057)*(1-0.00060) = 0.99804

(b)Mean cash intake = Loss at kth age*P(x=k) for k from 25 to 29

=99830*(0.00036) +99660*(0.00043) +99490*(0.00053) + 99320*(0.00057)+99150*(0.00060) = 247.6247

Profit = 850*0.99804 =848.334

Mean intake = 848.334 - 247.6247 =600.7093 = 600.71

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